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LIPSCHITZ REGULARITY FOR A HOMOGENEOUS DOUBLY NONLINEAR PDE
Univ Penn, Dept Math, Philadelphia, PA 19104 USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden.
2019 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 51, no 4, p. 3606-3624Article in journal (Refereed) Published
Abstract [en]

We study the doubly nonlinear PDE vertical bar partial derivative u vertical bar(p-2)partial derivative(t)u - div(vertical bar del u vertical bar(p-2)del u) = 0. This equation arises in the study of extremals of Poincare inequalities in Sobolev spaces. We prove spatial Lipschitz continuity and Holder continuity in time of order (p - 1)/p for viscosity solutions. As an application of our estimates, we obtain pointwise control of the large time behavior of solutions.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2019. Vol. 51, no 4, p. 3606-3624
Keywords [en]
doubly nonlinear PDE, viscosity solutions, regularity
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-394178DOI: 10.1137/19M1246201ISI: 000483950800026OAI: oai:DiVA.org:uu-394178DiVA, id: diva2:1357792
Funder
Swedish Research Council, 2012-3124Swedish Research Council, 2017-03736Available from: 2019-10-04 Created: 2019-10-04 Last updated: 2019-10-04Bibliographically approved

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